4k^2+42k+28=0

Solution for 4k^2+42k+28=0 equation:

4k^2+42k+28=0

a = 4; b = 42; c = +28;
Δ = b2-4ac
Δ = 422-4·4·28
Δ = 1316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1316}=\sqrt{4*329}=\sqrt{4}*\sqrt{329}=2\sqrt{329}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{329}}{2*4}=\frac{-42-2\sqrt{329}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{329}}{2*4}=\frac{-42+2\sqrt{329}}{8}
$